IODS Course Project
Justin Box
About the Project
This is Intro to Open Data Science. A course for everyone and a course for anywhere. The course runs for 7 weeks (Tue. 16-18:00) and consists of multiple on-line projects and assignments.
IODS Week 2
This weeks assignments included data wrangling and analysis!
Brief Description of Data
The data in this table is student responses to questions regarding 3 types of learning apporaches (Deep,Surface, and Strategic). The dataset also includes personal characteristics like age, gender. Students were asked several questions (scale 1-5) regarding each type of learning. The average of these responses is presented in the table.
Summary of Results
For this data set, 66% of respondents were female and 34% were male. Their ages ranged from 17-55 (mean 25.5) years old. Points ranged from 7-33 (mean 22.7) The average scale rating of “attitude”“,”deep“,”stra“, and”surf" was 3.1, 3.6, 3.1, and 2.7 respectively
Code
print(students2014) summary(students2014)
Regression Models
Code
library(ggplot2) qplot(attitude, points, data = students2014) + geom_smooth(method = “lm”)
fit a linear model
points_v_attitude <- lm(points ~ attitude, data = students2014)
print out a summary of the model
summary(points_v_attitude)
Interpretation
There is a statistically significant positive correlation between attitude and points (p=4.13e-09).The multiple R-squared value was 0.1906. This means that the strength of the correlation was relatively weak.
Diagnostic Plots
my_model2 <- lm(points ~ attitude + stra, data = students2014)
par(mfrow = c(2,2)) plot(my_model2, which = c(1,2,5))
These diagnostic plots test various aspects of the data such as normality, linearity, and the effect of outliers. These data appear to be normally distributed with a few outliers that could be affecting the linear regression model.
IODS Week 3
The Data
This data evaluates student achievement in secondary education of two Portuguese schools. The data attributes include student grades, demographic, social and school related features and it was collected by using school reports and questionnaires. Two datasets are provided regarding the performance in two distinct subjects: Mathematics (mat) and Portuguese language (por).
For this analysis, the two data sets were combined and only those cases with the same student’s repsonse in BOTH data sets were included.
Description of Variables
For full description of the variables Click Here
alc_use is the average of ‘Dalc’ and ‘Walc’ high_use is TRUE if ‘alc_use’ is higher than 2 and FALSE otherwise
The focus of this analysis is on the relationships between high/low alcohol consumption and selected other variables in the data
My Hypotheses
1) Parental education affects alcohol use
2) Study time affects alcohol use
3) Access to internet affects alcohol use
4) Address affects alcohol use
Analysis
alc <- read.csv(file = “alc.csv”, header=TRUE, sep=“,”)
Looking at Various Plots
##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union## Observations: 382
## Variables: 36
## $ X <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
## $ school <fct> GP, GP, GP, GP, GP, GP, GP, GP, GP, GP, GP, GP, GP,...
## $ sex <fct> F, F, F, F, F, M, M, F, M, M, F, F, M, M, M, F, F, ...
## $ age <int> 18, 17, 15, 15, 16, 16, 16, 17, 15, 15, 15, 15, 15,...
## $ address <fct> U, U, U, U, U, U, U, U, U, U, U, U, U, U, U, U, U, ...
## $ famsize <fct> GT3, GT3, LE3, GT3, GT3, LE3, LE3, GT3, LE3, GT3, G...
## $ Pstatus <fct> A, T, T, T, T, T, T, A, A, T, T, T, T, T, A, T, T, ...
## $ Medu <int> 4, 1, 1, 4, 3, 4, 2, 4, 3, 3, 4, 2, 4, 4, 2, 4, 4, ...
## $ Fedu <int> 4, 1, 1, 2, 3, 3, 2, 4, 2, 4, 4, 1, 4, 3, 2, 4, 4, ...
## $ Mjob <fct> at_home, at_home, at_home, health, other, services,...
## $ Fjob <fct> teacher, other, other, services, other, other, othe...
## $ reason <fct> course, course, other, home, home, reputation, home...
## $ nursery <fct> yes, no, yes, yes, yes, yes, yes, yes, yes, yes, ye...
## $ internet <fct> no, yes, yes, yes, no, yes, yes, no, yes, yes, yes,...
## $ guardian <fct> mother, father, mother, mother, father, mother, mot...
## $ traveltime <int> 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, ...
## $ studytime <int> 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 3, 1, 3, ...
## $ failures <int> 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
## $ schoolsup <fct> yes, no, yes, no, no, no, no, yes, no, no, no, no, ...
## $ famsup <fct> no, yes, no, yes, yes, yes, no, yes, yes, yes, yes,...
## $ paid <fct> no, no, yes, yes, yes, yes, no, no, yes, yes, yes, ...
## $ activities <fct> no, no, no, yes, no, yes, no, no, no, yes, no, yes,...
## $ higher <fct> yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, y...
## $ romantic <fct> no, no, no, yes, no, no, no, no, no, no, no, no, no...
## $ famrel <int> 4, 5, 4, 3, 4, 5, 4, 4, 4, 5, 3, 5, 4, 5, 4, 4, 3, ...
## $ freetime <int> 3, 3, 3, 2, 3, 4, 4, 1, 2, 5, 3, 2, 3, 4, 5, 4, 2, ...
## $ goout <int> 4, 3, 2, 2, 2, 2, 4, 4, 2, 1, 3, 2, 3, 3, 2, 4, 3, ...
## $ Dalc <int> 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
## $ Walc <int> 1, 1, 3, 1, 2, 2, 1, 1, 1, 1, 2, 1, 3, 2, 1, 2, 2, ...
## $ health <int> 3, 3, 3, 5, 5, 5, 3, 1, 1, 5, 2, 4, 5, 3, 3, 2, 2, ...
## $ absences <int> 5, 3, 8, 1, 2, 8, 0, 4, 0, 0, 1, 2, 1, 1, 0, 5, 8, ...
## $ G1 <int> 2, 7, 10, 14, 8, 14, 12, 8, 16, 13, 12, 10, 13, 11,...
## $ G2 <int> 8, 8, 10, 14, 12, 14, 12, 9, 17, 14, 11, 12, 14, 11...
## $ G3 <int> 8, 8, 11, 14, 12, 14, 12, 10, 18, 14, 12, 12, 13, 1...
## $ alc_use <dbl> 1.0, 1.0, 2.5, 1.0, 1.5, 1.5, 1.0, 1.0, 1.0, 1.0, 1...
## $ high_use <lgl> FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE, FAL...## Warning: attributes are not identical across measure variables;
## they will be dropped## Observations: 13,752
## Variables: 2
## $ key <chr> "X", "X", "X", "X", "X", "X", "X", "X", "X", "X", "X", "...
## $ value <chr> "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11",...## Warning: attributes are not identical across measure variables;
## they will be dropped
## # A tibble: 4 x 4
## # Groups: sex [?]
## sex high_use count mean_grade
## <fct> <lgl> <int> <dbl>
## 1 F FALSE 156 11.4
## 2 F TRUE 42 11.7
## 3 M FALSE 112 12.2
## 4 M TRUE 72 10.3
Including Plots
## Warning: attributes are not identical across measure variables;
## they will be dropped
Analysis: there appears to be a greater proportion of “high use” individuals who live in rural areas compared to urban.
Analysis: there appears to be a greater proportion of “high use” individuals who studied less than 2 hours per week
Logistic Regression
m <- glm(high_use ~ address + absences + studytime + failures, data = alc, family = “binomial”)
Summary of the Model
# print out a summary of the model
m <- glm(high_use ~ address + absences + studytime + failures, data = alc, family = "binomial")
summary(m)##
## Call:
## glm(formula = high_use ~ address + absences + studytime + failures,
## family = "binomial", data = alc)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.3106 -0.8274 -0.6498 1.1066 2.2127
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.03894 0.42264 0.092 0.926596
## addressU -0.49810 0.27809 -1.791 0.073268 .
## absences 0.07883 0.02288 3.446 0.000569 ***
## studytime -0.49431 0.15835 -3.122 0.001798 **
## failures 0.35312 0.19100 1.849 0.064487 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 465.68 on 381 degrees of freedom
## Residual deviance: 426.83 on 377 degrees of freedom
## AIC: 436.83
##
## Number of Fisher Scoring iterations: 4Deviance Residuals: Min 1Q Median 3Q Max
-1.5716 -0.7977 -0.6399 1.1262 2.1197
Coefficients of the Model
## Waiting for profiling to be done...## OR 2.5 % 97.5 %
## (Intercept) 1.0397050 0.4536726 2.3898611
## addressU 0.6076839 0.3532793 1.0542771
## absences 1.0820164 1.0367785 1.1342085
## studytime 0.6099923 0.4431742 0.8256399
## failures 1.4235086 0.9792692 2.0818432An odds ratio (OR) is a measure of association between an exposure and an outcome. The OR represents the odds that an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure.
Cross Tabulation
## prediction
## high_use FALSE TRUE
## FALSE 253 15
## TRUE 89 25
## prediction
## high_use FALSE TRUE Sum
## FALSE 0.66230366 0.03926702 0.70157068
## TRUE 0.23298429 0.06544503 0.29842932
## Sum 0.89528796 0.10471204 1.00000000Inaccurately Classified Individuals
## [1] 0.2722513The training error rate here is 27.2%.
Bonus: 10-Fold Cross Validation
## [1] 0.2827225Here the error rate is 28%.
IODS Week 4
Clustering and Classification
About the Data
This week, I investigated the Boston dataset which contains data of housing values in the suburbs of Boston. Boston dataset structure and dimensions are:
str(Boston)## 'data.frame': 506 obs. of 14 variables:
## $ crim : num 0.00632 0.02731 0.02729 0.03237 0.06905 ...
## $ zn : num 18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
## $ indus : num 2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
## $ chas : int 0 0 0 0 0 0 0 0 0 0 ...
## $ nox : num 0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
## $ rm : num 6.58 6.42 7.18 7 7.15 ...
## $ age : num 65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
## $ dis : num 4.09 4.97 4.97 6.06 6.06 ...
## $ rad : int 1 2 2 3 3 3 5 5 5 5 ...
## $ tax : num 296 242 242 222 222 222 311 311 311 311 ...
## $ ptratio: num 15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
## $ black : num 397 397 393 395 397 ...
## $ lstat : num 4.98 9.14 4.03 2.94 5.33 ...
## $ medv : num 24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...dim(Boston)## [1] 506 14All variables are further explained HERE.
Graphing the Data
pairs(Boston, lower.panel = NULL)
This representation is difficult to interpret, so next, I will use a correlation matrix to more easily visualize the data.
cor_matrix<-cor(Boston) %>% round(digits=2)
corrplot(cor_matrix, method="circle", type = "upper", cl.pos = "b", tl.pos = "d", tl.cex = 0.6)
Here, it is much easier to see the correlations. According to this matrix rad (index of accessibility to radial highways) and tax (full-value property-tax rate per $10,000) have the highest positive correlation.
Standardizing the Data
After scaling, the summary of the data is now available:
summary(boston_scaled)## crim zn indus
## Min. :-0.419367 Min. :-0.48724 Min. :-1.5563
## 1st Qu.:-0.410563 1st Qu.:-0.48724 1st Qu.:-0.8668
## Median :-0.390280 Median :-0.48724 Median :-0.2109
## Mean : 0.000000 Mean : 0.00000 Mean : 0.0000
## 3rd Qu.: 0.007389 3rd Qu.: 0.04872 3rd Qu.: 1.0150
## Max. : 9.924110 Max. : 3.80047 Max. : 2.4202
## chas nox rm age
## Min. :-0.2723 Min. :-1.4644 Min. :-3.8764 Min. :-2.3331
## 1st Qu.:-0.2723 1st Qu.:-0.9121 1st Qu.:-0.5681 1st Qu.:-0.8366
## Median :-0.2723 Median :-0.1441 Median :-0.1084 Median : 0.3171
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.:-0.2723 3rd Qu.: 0.5981 3rd Qu.: 0.4823 3rd Qu.: 0.9059
## Max. : 3.6648 Max. : 2.7296 Max. : 3.5515 Max. : 1.1164
## dis rad tax ptratio
## Min. :-1.2658 Min. :-0.9819 Min. :-1.3127 Min. :-2.7047
## 1st Qu.:-0.8049 1st Qu.:-0.6373 1st Qu.:-0.7668 1st Qu.:-0.4876
## Median :-0.2790 Median :-0.5225 Median :-0.4642 Median : 0.2746
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.6617 3rd Qu.: 1.6596 3rd Qu.: 1.5294 3rd Qu.: 0.8058
## Max. : 3.9566 Max. : 1.6596 Max. : 1.7964 Max. : 1.6372
## black lstat medv
## Min. :-3.9033 Min. :-1.5296 Min. :-1.9063
## 1st Qu.: 0.2049 1st Qu.:-0.7986 1st Qu.:-0.5989
## Median : 0.3808 Median :-0.1811 Median :-0.1449
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.4332 3rd Qu.: 0.6024 3rd Qu.: 0.2683
## Max. : 0.4406 Max. : 3.5453 Max. : 2.9865Now the data is normalized and mean centerd.
Next, I created a categorical variable crime of the crime rate (crim) by using its quantiles as break points. Then, I removed the old crime rate variable (crim) from the dataset and added the new variable crime. This was done with the following R code:
boston_scaled <- as.data.frame(boston_scaled)
bins <- quantile(boston_scaled$crim)
crime <- cut(boston_scaled$crim, breaks = bins, include.lowest = TRUE, label=c("low","med_low","med_high","high"))
boston_scaled <- dplyr::select(boston_scaled, -crim)
boston_scaled <- data.frame(boston_scaled, crime)The final step before performing the Linear Discriminant Analysis (LDA) is to separate the dataset into training (train) and testing (test) sets with a ratio of 4:1.
n <- nrow(boston_scaled)
ind <- sample(n, size = n * 0.8)
train <- boston_scaled[ind,]
test <- boston_scaled[-ind,]Linear Discriminant Analysis
Next, I used the LDA on the training set train. This involves using the categorical crime rate crime as the target variable and all other variables as predictor variables.
lda.fit <- lda(crime ~ ., data = train)
classes <- as.numeric(train$crime)
plot(lda.fit, dimen = 2, col = classes, pch = classes)
Here you can see that the high crime rate grouped more closely than the others.
Making Predictions
First, I saved the crime categories from the test set and then removed the categorical crime variable from the test dataset.
correct_classes <- test$crime
test <- dplyr::select(test, -crime)
lda.pred <- predict(lda.fit, newdata = test)Now I can cross tabulate the results with the crime categories from the test set.
table(correct = correct_classes, predicted = lda.pred$class)## predicted
## correct low med_low med_high high
## low 20 11 0 0
## med_low 6 14 0 0
## med_high 0 10 17 1
## high 0 0 0 23From this table, we can see that the predicitons are fairly accurate depending on the category. In this model, the high was correctly predicted 25 times and incorrectly only 1. Med-high, however, was correctly predicted 14 times and incorrectly 5 times (4 in med_low and 1 in low).
CLusters/Distance Measures
First, the dataset “Boston” has to be re-loaded and re-scaled.
data("Boston")
boston_scaled <- scale(Boston)
boston_scaled <- as.data.frame(boston_scaled)Using the euclidean and manhattan distances, the distance between observations can be measured. Then, a k-means algorithm can be run on the dataset.
km <-kmeans(boston_scaled, centers = 5)
summary(km)## Length Class Mode
## cluster 506 -none- numeric
## centers 70 -none- numeric
## totss 1 -none- numeric
## withinss 5 -none- numeric
## tot.withinss 1 -none- numeric
## betweenss 1 -none- numeric
## size 5 -none- numeric
## iter 1 -none- numeric
## ifault 1 -none- numericFinally, I can investigate the optimal number of clusters then run the algorithm again.
k_max <- 10
twcss <- sapply(1:k_max, function(k){kmeans(boston_scaled, k)$tot.withinss})
qplot(x = 1:k_max, y = twcss, geom = 'line')
It seems that the WCSS decreases significantly between 2-3, so I tried with just 2 clusters.
km <-kmeans(boston_scaled, centers = 2)
pairs(boston_scaled[3:7], col = km$cluster, lower.panel = NULL)
km <-kmeans(boston_scaled, centers = 3)
pairs(boston_scaled[3:7], col = km$cluster, lower.panel = NULL)
With just visual inspection, it appears that 2 clusters appears to be the best option.
library(dplyr)
library(tidyr)
library(ggplot2)
library(corrplot)
library(GGally)
library(FactoMineR)
options(scipen=999)IODS Week 5
Description of the Data
“HDI.Rank” = Country rank in Human Development Index “Country”
“HDI” = Human Development Index
“L.Exp.Birth” = Life expectancy at birth
“Exp.Yr.Ed” = Expected years of schooling
“Mean.Yr.Ed” = Mean years of schooling
“GNIperCap” = Gross national income (GNI) per capita
“GNIperCap-HDI.Rank” = Gross national income (GNI) per capita - Human Development Index “GII.Rank”= Country rank in Gender Inequality Index “GII” = Gender Inequality Index
“Mat.Mort.Rat” = Maternal mortality ratio
“Ad.Birth.Rate” = Adolescent birth rate
“%Rep.in.Par” = Percetange of female representatives in parliament
“Pop.w.2nd.Ed.F” = Population of women with at least some secondary education “Pop.w.2nd.Ed.M” = Population of men with at least some secondary education “Lab.Part.Rate.F” = Population of women participating in labor “Lab.Part.Rate.M” = Population of men participating in labor “Edu2.FM” = The ratio of Female / Male populations with secondary education (edu2F / edu2M) “Labo.FM” = The ratio of Female / Male participation in labour force (work2F / work2M)
More information about the dataset can be found here and here.
url = "http://s3.amazonaws.com/assets.datacamp.com/production/course_2218/datasets/human2.txt"
human <- read.table(url, sep=",", header=TRUE)Visualization
In this graph, blue circles indicate positive correlations and red indicate negative. Size and intensity of the circle reflect the strength of the correlation.
# calculate the correlation matrix and round it
cor_matrix<-cor(human) %>% round(digits = 2)
# visualize the correlation matrix
corrplot.mixed(cor_matrix, number.cex = .7, tl.pos = "d", tl.cex = 0.6)
From this graph, we can see that there is a strong correlation between education Edu.Exp and life expectancy Life.Exp, GNI, maternal mortality Mat.Mor and adolescent birth rate Ado.Birth. Life expectancy Life.Exp is naturally linked to Mat.Mor and Ado.Birth (negative).
Principal Component Analysis
A principal component analysis (PCA) is first performed on the non-standardized data. The following biplot shows the observations by the first two principal components (PC1, PC2). The arrow and its length represent the correlation between the feature and the corresponding principal component.
GNI appears to be the only varaible correlated to PC1. However, this is due to its large range compared to others within the dataset. This affects the interpretation of the plot and which variables hare actually having an effect.
The dataset is then re-standardized and PCA done again. Here is the summary of the new normalized dataset:
## Edu2.FM Labo.FM Edu.Exp Life.Exp
## Min. :-2.8189 Min. :-2.6247 Min. :-2.7378 Min. :-2.7188
## 1st Qu.:-0.5233 1st Qu.:-0.5484 1st Qu.:-0.6782 1st Qu.:-0.6425
## Median : 0.3503 Median : 0.2316 Median : 0.1140 Median : 0.3056
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.5958 3rd Qu.: 0.7350 3rd Qu.: 0.7126 3rd Qu.: 0.6717
## Max. : 2.6646 Max. : 1.6632 Max. : 2.4730 Max. : 1.4218
## GNI Mat.Mor Ado.Birth Parli.F
## Min. :-0.9193 Min. :-0.6992 Min. :-1.1325 Min. :-1.8203
## 1st Qu.:-0.7243 1st Qu.:-0.6496 1st Qu.:-0.8394 1st Qu.:-0.7409
## Median :-0.3013 Median :-0.4726 Median :-0.3298 Median :-0.1403
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.3712 3rd Qu.: 0.1932 3rd Qu.: 0.6030 3rd Qu.: 0.6127
## Max. : 5.6890 Max. : 4.4899 Max. : 3.8344 Max. : 3.1850The biplot is drawn again but this time using the scaled dataset.
Education Edu.Exp, Edu2.FM is negatively correlated to adolescent birth Ado.Birth, while life expectancy Life.Exp is negatively correlated to maternal mortality Mat.Mor. Gross national income GNI directly goes together with education and life expectancy, while against mortality and teenage birth, as expected. Female anticipation in parliment Parli.F can be somewhat related to ratio of female and male in the workforce Labo.FM.
Interpretation
Because Parli.F and Labo.FM align with PC2, and Edu.Exp, Edu2.FM, Life.Exp,GNI, Mat.Mor and Ado.Birth align with PC1, it can be inferred that the principal components have their implicit meanings.
For PC1, it’s understandable to see education, income and life expectancy being related as they complement each other in real life. Poor education could lead to lack of opportunity and/or upward social mobility and therefore high adolescent birth rate, and subsequently maternal mortality. This mortality also directly affects life expectancy.
This principal component PC1 therefore reflects Health and knowledge and its effects.
For PC2, it’s more about Gender empowerment. It could be inferred that as females become more prominent in the workforce, they end up being more politically active, which is a common finding in countries where gender equality is well documented.
Tea Dataset
The tea dataset from FactoMineR library contains a very comprehensive research on how tea is consumed, including where, how, in which environment, etc. age is the only variable with integer values, while the rest contain categorical values, which are self-explanatory.
Loading the Data
## 'data.frame': 300 obs. of 36 variables:
## $ breakfast : Factor w/ 2 levels "breakfast","Not.breakfast": 1 1 2 2 1 2 1 2 1 1 ...
## $ tea.time : Factor w/ 2 levels "Not.tea time",..: 1 1 2 1 1 1 2 2 2 1 ...
## $ evening : Factor w/ 2 levels "evening","Not.evening": 2 2 1 2 1 2 2 1 2 1 ...
## $ lunch : Factor w/ 2 levels "lunch","Not.lunch": 2 2 2 2 2 2 2 2 2 2 ...
## $ dinner : Factor w/ 2 levels "dinner","Not.dinner": 2 2 1 1 2 1 2 2 2 2 ...
## $ always : Factor w/ 2 levels "always","Not.always": 2 2 2 2 1 2 2 2 2 2 ...
## $ home : Factor w/ 2 levels "home","Not.home": 1 1 1 1 1 1 1 1 1 1 ...
## $ work : Factor w/ 2 levels "Not.work","work": 1 1 2 1 1 1 1 1 1 1 ...
## $ tearoom : Factor w/ 2 levels "Not.tearoom",..: 1 1 1 1 1 1 1 1 1 2 ...
## $ friends : Factor w/ 2 levels "friends","Not.friends": 2 2 1 2 2 2 1 2 2 2 ...
## $ resto : Factor w/ 2 levels "Not.resto","resto": 1 1 2 1 1 1 1 1 1 1 ...
## $ pub : Factor w/ 2 levels "Not.pub","pub": 1 1 1 1 1 1 1 1 1 1 ...
## $ Tea : Factor w/ 3 levels "black","Earl Grey",..: 1 1 2 2 2 2 2 1 2 1 ...
## $ How : Factor w/ 4 levels "alone","lemon",..: 1 3 1 1 1 1 1 3 3 1 ...
## $ sugar : Factor w/ 2 levels "No.sugar","sugar": 2 1 1 2 1 1 1 1 1 1 ...
## $ how : Factor w/ 3 levels "tea bag","tea bag+unpackaged",..: 1 1 1 1 1 1 1 1 2 2 ...
## $ where : Factor w/ 3 levels "chain store",..: 1 1 1 1 1 1 1 1 2 2 ...
## $ price : Factor w/ 6 levels "p_branded","p_cheap",..: 4 6 6 6 6 3 6 6 5 5 ...
## $ age : int 39 45 47 23 48 21 37 36 40 37 ...
## $ sex : Factor w/ 2 levels "F","M": 2 1 1 2 2 2 2 1 2 2 ...
## $ SPC : Factor w/ 7 levels "employee","middle",..: 2 2 4 6 1 6 5 2 5 5 ...
## $ Sport : Factor w/ 2 levels "Not.sportsman",..: 2 2 2 1 2 2 2 2 2 1 ...
## $ age_Q : Factor w/ 5 levels "15-24","25-34",..: 3 4 4 1 4 1 3 3 3 3 ...
## $ frequency : Factor w/ 4 levels "1/day","1 to 2/week",..: 1 1 3 1 3 1 4 2 3 3 ...
## $ escape.exoticism: Factor w/ 2 levels "escape-exoticism",..: 2 1 2 1 1 2 2 2 2 2 ...
## $ spirituality : Factor w/ 2 levels "Not.spirituality",..: 1 1 1 2 2 1 1 1 1 1 ...
## $ healthy : Factor w/ 2 levels "healthy","Not.healthy": 1 1 1 1 2 1 1 1 2 1 ...
## $ diuretic : Factor w/ 2 levels "diuretic","Not.diuretic": 2 1 1 2 1 2 2 2 2 1 ...
## $ friendliness : Factor w/ 2 levels "friendliness",..: 2 2 1 2 1 2 2 1 2 1 ...
## $ iron.absorption : Factor w/ 2 levels "iron absorption",..: 2 2 2 2 2 2 2 2 2 2 ...
## $ feminine : Factor w/ 2 levels "feminine","Not.feminine": 2 2 2 2 2 2 2 1 2 2 ...
## $ sophisticated : Factor w/ 2 levels "Not.sophisticated",..: 1 1 1 2 1 1 1 2 2 1 ...
## $ slimming : Factor w/ 2 levels "No.slimming",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ exciting : Factor w/ 2 levels "exciting","No.exciting": 2 1 2 2 2 2 2 2 2 2 ...
## $ relaxing : Factor w/ 2 levels "No.relaxing",..: 1 1 2 2 2 2 2 2 2 2 ...
## $ effect.on.health: Factor w/ 2 levels "effect on health",..: 2 2 2 2 2 2 2 2 2 2 ...## [1] 300 36Variable Selection
Next, 6 variables were selected: “Tea”, “How”, “how”, “sugar”, “where”, “lunch”. These will be the focus of my analysis.
Multiple Correspondence Analysis
The table below is a summary of the MCA model performed on the tea dataset. As can be seen from the categorical variables, the way tea is packaged how and where it is used are closely related to Dim.1, as well as Dim.2. Meanwhile, the kind of Tea and How they are drank are related to Dim.3.
##
## Call:
## MCA(X = tea_time, graph = FALSE)
##
##
## Eigenvalues
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6
## Variance 0.279 0.261 0.219 0.189 0.177 0.156
## % of var. 15.238 14.232 11.964 10.333 9.667 8.519
## Cumulative % of var. 15.238 29.471 41.435 51.768 61.434 69.953
## Dim.7 Dim.8 Dim.9 Dim.10 Dim.11
## Variance 0.144 0.141 0.117 0.087 0.062
## % of var. 7.841 7.705 6.392 4.724 3.385
## Cumulative % of var. 77.794 85.500 91.891 96.615 100.000
##
## Individuals (the 10 first)
## Dim.1 ctr cos2 Dim.2 ctr cos2 Dim.3
## 1 | -0.298 0.106 0.086 | -0.328 0.137 0.105 | -0.327
## 2 | -0.237 0.067 0.036 | -0.136 0.024 0.012 | -0.695
## 3 | -0.369 0.162 0.231 | -0.300 0.115 0.153 | -0.202
## 4 | -0.530 0.335 0.460 | -0.318 0.129 0.166 | 0.211
## 5 | -0.369 0.162 0.231 | -0.300 0.115 0.153 | -0.202
## 6 | -0.369 0.162 0.231 | -0.300 0.115 0.153 | -0.202
## 7 | -0.369 0.162 0.231 | -0.300 0.115 0.153 | -0.202
## 8 | -0.237 0.067 0.036 | -0.136 0.024 0.012 | -0.695
## 9 | 0.143 0.024 0.012 | 0.871 0.969 0.435 | -0.067
## 10 | 0.476 0.271 0.140 | 0.687 0.604 0.291 | -0.650
## ctr cos2
## 1 0.163 0.104 |
## 2 0.735 0.314 |
## 3 0.062 0.069 |
## 4 0.068 0.073 |
## 5 0.062 0.069 |
## 6 0.062 0.069 |
## 7 0.062 0.069 |
## 8 0.735 0.314 |
## 9 0.007 0.003 |
## 10 0.643 0.261 |
##
## Categories (the 10 first)
## Dim.1 ctr cos2 v.test Dim.2 ctr
## black | 0.473 3.288 0.073 4.677 | 0.094 0.139
## Earl Grey | -0.264 2.680 0.126 -6.137 | 0.123 0.626
## green | 0.486 1.547 0.029 2.952 | -0.933 6.111
## alone | -0.018 0.012 0.001 -0.418 | -0.262 2.841
## lemon | 0.669 2.938 0.055 4.068 | 0.531 1.979
## milk | -0.337 1.420 0.030 -3.002 | 0.272 0.990
## other | 0.288 0.148 0.003 0.876 | 1.820 6.347
## tea bag | -0.608 12.499 0.483 -12.023 | -0.351 4.459
## tea bag+unpackaged | 0.350 2.289 0.056 4.088 | 1.024 20.968
## unpackaged | 1.958 27.432 0.523 12.499 | -1.015 7.898
## cos2 v.test Dim.3 ctr cos2 v.test
## black 0.003 0.929 | -1.081 21.888 0.382 -10.692 |
## Earl Grey 0.027 2.867 | 0.433 9.160 0.338 10.053 |
## green 0.107 -5.669 | -0.108 0.098 0.001 -0.659 |
## alone 0.127 -6.164 | -0.113 0.627 0.024 -2.655 |
## lemon 0.035 3.226 | 1.329 14.771 0.218 8.081 |
## milk 0.020 2.422 | 0.013 0.003 0.000 0.116 |
## other 0.102 5.534 | -2.524 14.526 0.197 -7.676 |
## tea bag 0.161 -6.941 | -0.065 0.183 0.006 -1.287 |
## tea bag+unpackaged 0.478 11.956 | 0.019 0.009 0.000 0.226 |
## unpackaged 0.141 -6.482 | 0.257 0.602 0.009 1.640 |
##
## Categorical variables (eta2)
## Dim.1 Dim.2 Dim.3
## Tea | 0.126 0.108 0.410 |
## How | 0.076 0.190 0.394 |
## how | 0.708 0.522 0.010 |
## sugar | 0.065 0.001 0.336 |
## where | 0.702 0.681 0.055 |
## lunch | 0.000 0.064 0.111 |The factor map below show the correlation between variables in Dim.1 and Dim.2. From this map, we see tea bag is closely related to chain store, while unpackaged tea anad tea shop are closely related. Earl Grey is usually served with milk, while black tea can be served with either milk, lemon or alone.
